IntroR: Final Report Analysis

1. Introduction

In this notebook, I examine the relationship between utterance fluency (UF) measures and L2 speaking anxiety, addressing the following three research questions (RQs):

• RQ1: To what extent are speed fluency measures associated with cognitive, somatic, and behavioral speaking anxiety?

• RQ2: To what extent are breakdown fluency measures associated with cognitive, somatic, and behavioral speaking anxiety?

• RQ3: To what extent are repair fluency measures associated with cognitive, somatic, and behavioral speaking anxiety?

In the following sections, I preprocess data, conduct preliminary analyses, and construct regression models.

The following code block loads R packages required for analyses.

---

2. Data Preprocess

This section tidies data. First of all, the following code block loads data of UF measures.

The current analysis focuses on the UF measures shown in Table 1.

Table 1. UF Dimension and Corresponding Measures

UF Dimension	Measure
Speed Fluency (SF)	Articulation Rate (AR)
Breakdown Fluency (BDF)	Mid-Clause Pause Ratio (MCPR)
	End-Clause Pause Ratio (ECPR)
	Mid-Clause Pause Duration (MCPD)
	End-Clause Pause Duration (ECPD)
Repair Fluency (RF)	Disfluency Ratio

Thus, the following code block selects target measures. The code block also renames the columns filename and dysfluency_ratio to participant_id and disfluency_ratio, respectively.

Next, the following code block loads data of post questionnaire about anxiety and linguistic background.

The following code block selects columns related to participant ID, anxiety, L2 English proficiency, and other backgrounds and renames them.

---

3. Preliminary Analysis

3.1. Participant Background

The following code block calculates the descriptive statistics of participants’ age.

df_questionnaire_tidy %>%
  select(age) %>%
  skim()

── Data Summary ────────────────────────
                           Values    
Name                       Piped data
Number of rows             10        
Number of columns          1         
_______________________              
Column type frequency:               
  numeric                  1         
________________________             
Group variables            None      

The result showed that participants’ age was ranged \([20, 38]\), and their mean and SD were \(28.8\) and \(5.613\).

The following code block counts sex of participants.

df_questionnaire_tidy %>%
  group_by(sex) %>%
  summarize(N = n())

The result indicated that there were equal number of male and female participants.

3.2. Proficiency Levels

The following code block converts L2 English assessment scores to CEFR.

cefr_levels = c("A1", "A2", "B1", "B2", "C1", "C2")

df_questionnaire_tidy %>%
  select(participant_id, TOEFL_IBT, IELTS, TOEIC, eiken) %>%
  mutate(
    TOEFL_IBT = case_when(
      TOEFL_IBT >= 114 ~ "C2",
      TOEFL_IBT >= 95 ~ "C1",
      TOEFL_IBT >= 72 ~ "B2"
    ),
    IELTS = case_when(
      IELTS >= 7 ~ "C1"
    ),
    TOEIC = case_when(
      TOEIC >= 945 ~ "C1",
      TOEIC >= 785 ~ "B1",
      TOEIC >= 550 ~ "B2"
    ),
    eiken = case_when(
      eiken >= 3 ~ "A1",
      eiken >= 2 ~ "B1",
      eiken >= 1.5 ~ "B2",
      eiken >= 1 ~ "C1"
    )
  ) %>%
  mutate(
    TOEFL_IBT = factor(TOEFL_IBT, levels = cefr_levels, order = T),
    IELTS = factor(IELTS, levels = cefr_levels, order = T),
    TOEIC = factor(TOEIC, levels = cefr_levels, order = T),
    eiken = factor(eiken, levels = cefr_levels, order = T)
  ) %>% 
  replace_na(list(
    TOEFL_IBT = "A1",
    IELTS = "A1",
    TOEIC = "A1",
    eiken = "A1"
  )) %>%
  group_by(participant_id) %>%
  summarize(CEFR = max(TOEFL_IBT, IELTS, TOEIC, eiken)) %>%
  group_by(CEFR) %>%
  summarize(N = n())

The result suggested that most participants were advanced-level L2 English learners (\(N=6\)), while other four participants were intermediate-level English learners.

3.3. UF Measures

The following code block calculates the descriptive statistics of UF measures.

df_uf_tidy %>%
  select(-c(participant_id)) %>%
  skim()

── Data Summary ────────────────────────
                           Values    
Name                       Piped data
Number of rows             10        
Number of columns          6         
_______________________              
Column type frequency:               
  numeric                  6         
________________________             
Group variables            None      

3.4. Speaking Anxiety

The following code blocks calculate the reliability of anxiety questionnaire answers in terms of Cronbach’s \(\alpha\).

3.4.1. Reliability of Cognitive Anxiety

df_questionnaire_tidy %>% 
  select(
    cognitive_anxiety_1,
    cognitive_anxiety_2,
    cognitive_anxiety_3
  ) %>%
  alpha()

Reliability analysis   
Call: alpha(x = .)

 

    95% confidence boundaries 

 Reliability if an item is dropped:

 Item statistics 

Non missing response frequency for each item
                      1   2   3   4   5 miss
cognitive_anxiety_1 0.0 0.3 0.1 0.3 0.3    0
cognitive_anxiety_2 0.1 0.1 0.0 0.6 0.2    0
cognitive_anxiety_3 0.2 0.3 0.0 0.2 0.3    0

The Cornbach’s \(\alpha\) of cognitive anxiety questionnaires was \(.747\), indicating an acceptable internal consistency

3.4.2. Reliability of Somatic Anxiety

df_questionnaire_tidy %>% 
  select(
    somatic_anxiety_1,
    somatic_anxiety_2,
    somatic_anxiety_3
  ) %>%
  alpha()

Reliability analysis   
Call: alpha(x = .)

 

    95% confidence boundaries 

 Reliability if an item is dropped:

 Item statistics 

Non missing response frequency for each item
                    1   2   3   4   5 miss
somatic_anxiety_1 0.2 0.3 0.1 0.2 0.2    0
somatic_anxiety_2 0.3 0.2 0.2 0.0 0.3    0
somatic_anxiety_3 0.3 0.3 0.0 0.4 0.0    0

The Cornbach’s \(\alpha\) of somatic anxiety questionnaires was \(.900\), indicating a excellent internal consistency.

3.4.3. Behavioral Anxiety

df_questionnaire_tidy %>% 
  select(
    behavioral_anxiety_1,
    behavioral_anxiety_2,
    behavioral_anxiety_3
  ) %>%
  alpha()

Reliability analysis   
Call: alpha(x = .)

 

    95% confidence boundaries 

 Reliability if an item is dropped:

 Item statistics 

Non missing response frequency for each item
                       1   2   3   4   5 miss
behavioral_anxiety_1 0.2 0.4 0.2 0.1 0.1    0
behavioral_anxiety_2 0.2 0.3 0.1 0.3 0.1    0
behavioral_anxiety_3 0.4 0.3 0.2 0.1 0.0    0

The Cornbach’s \(\alpha\) of somatic anxiety questionnaires was \(.814\), indicating a good internal consistency.

3.5. Correlations

This subsection conducts correlation analyses between UF measures and speaking anxiety. Before the analyses, the following code block calculates three anxiety scores by summing items and joins the two dataframes.

df_questionnaire_tidy %>%
  group_by(participant_id) %>%
  summarize(
    cognitive_anxiety = sum(
      cognitive_anxiety_1, cognitive_anxiety_2, cognitive_anxiety_3
    ),
    somatic_anxiety = sum(
      somatic_anxiety_1, somatic_anxiety_2, somatic_anxiety_3
    ),
    behavioral_anxiety = sum(
      behavioral_anxiety_1, behavioral_anxiety_2, behavioral_anxiety_3
    )
  ) %>% 
  inner_join(
    df_uf_tidy, by = "participant_id"
  ) -> df_uf_anxiety

df_uf_anxiety

The following code block calculates the descriptive statistics of anxiety scores.

df_uf_anxiety %>%
  select(cognitive_anxiety, somatic_anxiety, behavioral_anxiety) %>%
  skim()

── Data Summary ────────────────────────
                           Values    
Name                       Piped data
Number of rows             10        
Number of columns          3         
_______________________              
Column type frequency:               
  numeric                  3         
________________________             
Group variables            None      

The following code block saves the concatenated dataframe as a csv file.

write.csv(df_uf_anxiety, here("data", "processed", "uf_anxiety.csv"))

3.5.1. Correlations Among Anxiety Scores

The following code block generates a correlation matrix of three anxiety scores.

df_uf_anxiety %>%
  select(
    cognitive_anxiety,
    somatic_anxiety,
    behavioral_anxiety
  ) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)

The result showed that significant strong correlation between cognitive and somatic anxiety (\(r=.78\)). In addition, there was slightly significant medium correlation between somatic and behavioral anxiety (\(r=.59\)). Meanwhile, there was small correlation between cognitive and behavioral anxiety (\(r=.48\)), but statistical significance was not found.

3.5.2. Correlations Between UF Measures and Cognitive Anxiety

The following code block generates a correlation matrix of UF measures and cognitive anxiety.

df_uf_anxiety %>%
  select(-c(
    participant_id, 
    somatic_anxiety, 
    behavioral_anxiety
  )) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)

The result showed significant large correlation between cognitive anxiety and ECPR, suggesting that participants produced end-clause pauses more frequently when cognitive anxiety was lower.

3.5.3. Correlations Between UF Measures and Somatic Anxiety

The following code block generates a correlation matrix of UF measures and somatic anxiety.

df_uf_anxiety %>%
  select(-c(
    participant_id, 
    cognitive_anxiety, 
    behavioral_anxiety
  )) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)

The result did not show significant correlations between somatic anxiety and UF measures.

3.5.4. Correlations Between UF Measures and Behavioral Anxiety

The following code block generates a correlation matrix of UF measures and behavioral anxiety.

df_uf_anxiety %>%
  select(-c(
    participant_id, 
    cognitive_anxiety, 
    somatic_anxiety
  )) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)

The result identified significant large correlations between behavioral anxiety and MCPD (\(r=-.76\)) and ECPD (\(r=.79\)), suggesting that participants who perceived lower behavioral anxiety generate longer MCPD and ECPD.

---

4. Regression Analyses

4.1. SF ~ Speaking Anxiety

The following code block constructs a regression model between AR and speaking anxiety.

model_ar <- lm(
  articulation_rate ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety
)

The following code block shows the result.

tab_model(model_ar, digits = 3)

The result did not show significant relationship between three anxiety scores and AR.

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ar)

Package `see` required for model diagnostic plots.

Registered S3 method overwritten by 'rmarkdown':
  method         from
  print.paged_df     

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$VIF
# Check for Multicollinearity

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220 -0.4923973 0.4307377 0.4604779
221 -0.4902838 0.4312372 0.4616089
222 -0.4881704 0.4317366 0.4627378
223 -0.4860570 0.4322333 0.4638646
224 -0.4839436 0.4327250 0.4649891
225 -0.4818302 0.4332167 0.4661115
226 -0.4797167 0.4337051 0.4672317
227 -0.4776033 0.4341890 0.4683496
228 -0.4754899 0.4346729 0.4694653
229 -0.4733765 0.4351530 0.4705786
230 -0.4712631 0.4356290 0.4716896
231 -0.4691496 0.4361050 0.4727983
232 -0.4670362 0.4365768 0.4739045
233 -0.4649228 0.4370449 0.4750083
234 -0.4628094 0.4375130 0.4761097
235 -0.4606960 0.4379765 0.4772085
236 -0.4585825 0.4384366 0.4783049
237 -0.4564691 0.4388968 0.4793987
238 -0.4543557 0.4393518 0.4804900
239 -0.4522423 0.4398039 0.4815787
240 -0.4501289 0.4402561 0.4826647
241 -0.4480154 0.4407027 0.4837481
242 -0.4459020 0.4411468 0.4848288
243 -0.4437886 0.4415909 0.4859068
244 -0.4416752 0.4420290 0.4869820
245 -0.4395618 0.4424651 0.4880545
246 -0.4374483 0.4429012 0.4891242
247 -0.4353349 0.4433306 0.4901910
248 -0.4332215 0.4437586 0.4912550
249 -0.4311081 0.4441866 0.4923161
250 -0.4289947 0.4446075 0.4933743
251 -0.4268812 0.4450274 0.4944296
252 -0.4247678 0.4454473 0.4954818
253 -0.4226544 0.4458595 0.4965311
254 -0.4205410 0.4462712 0.4975774
255 -0.4184276 0.4466830 0.4986206
256 -0.4163141 0.4470866 0.4996607
257 -0.4142007 0.4474901 0.5006977
258 -0.4120873 0.4478933 0.5017315
259 -0.4099739 0.4482886 0.5027622
260 -0.4078605 0.4486839 0.5037897
261 -0.4057470 0.4490784 0.5048139
262 -0.4036336 0.4494654 0.5058349
263 -0.4015202 0.4498525 0.5068526
264 -0.3994068 0.4502383 0.5078671
265 -0.3972934 0.4506171 0.5088781
266 -0.3951799 0.4509959 0.5098858
267 -0.3930665 0.4513729 0.5108901
268 -0.3909531 0.4517434 0.5118910
269 -0.3888397 0.4521140 0.5128884
270 -0.3867263 0.4524822 0.5138824
271 -0.3846128 0.4528444 0.5148728
272 -0.3824994 0.4532066 0.5158597
273 -0.3803860 0.4535661 0.5168431
274 -0.3782726 0.4539200 0.5178229
275 -0.3761592 0.4542739 0.5187990
276 -0.3740457 0.4546245 0.5197715
277 -0.3719323 0.4549701 0.5207403
278 -0.3698189 0.4553156 0.5217055
279 -0.3677055 0.4556574 0.5226669
280 -0.3655921 0.4559946 0.5236245
281 -0.3634786 0.4563318 0.5245784
282 -0.3613652 0.4566647 0.5255284
283 -0.3592518 0.4569936 0.5264747
284 -0.3571384 0.4573224 0.5274170
285 -0.3550250 0.4576465 0.5283555
286 -0.3529115 0.4579669 0.5292901
287 -0.3507981 0.4582873 0.5302207
288 -0.3486847 0.4586025 0.5311473
289 -0.3465713 0.4589145 0.5320700
290 -0.3444579 0.4592266 0.5329886
291 -0.3423444 0.4595329 0.5339032
292 -0.3402310 0.4598365 0.5348137
293 -0.3381176 0.4601401 0.5357201
294 -0.3360042 0.4604375 0.5366224
295 -0.3338908 0.4607327 0.5375206
296 -0.3317773 0.4610279 0.5384145
297 -0.3296639 0.4613164 0.5393043
298 -0.3275505 0.4616031 0.5401898
299 -0.3254371 0.4618899 0.5410711
300 -0.3233237 0.4621695 0.5419481
301 -0.3212102 0.4624478 0.5428207
302 -0.3190968 0.4627261 0.5436891
303 -0.3169834 0.4629968 0.5445531
304 -0.3148700 0.4632667 0.5454127
305 -0.3127566 0.4635366 0.5462679
306 -0.3106431 0.4637983 0.5471187
307 -0.3085297 0.4640597 0.5479650
308 -0.3064163 0.4643210 0.5488068
309 -0.3043029 0.4645740 0.5496442
310 -0.3021895 0.4648270 0.5504769
311 -0.3000760 0.4650793 0.5513052
312 -0.2979626 0.4653238 0.5521289
313 -0.2958492 0.4655684 0.5529479
314 -0.2937358 0.4658118 0.5537623
315 -0.2916224 0.4660478 0.5545721
316 -0.2895089 0.4662839 0.5553772
317 -0.2873955 0.4665184 0.5561776
318 -0.2852821 0.4667460 0.5569733
319 -0.2831687 0.4669737 0.5577642
320 -0.2810553 0.4671992 0.5585504
321 -0.2789418 0.4674184 0.5593318
322 -0.2768284 0.4676376 0.5601083
323 -0.2747150 0.4678542 0.5608800
324 -0.2726016 0.4680650 0.5616469
325 -0.2704882 0.4682758 0.5624088
326 -0.2683747 0.4684835 0.5631659
327 -0.2662613 0.4686858 0.5639180
328 -0.2641479 0.4688881 0.5646652
329 -0.2620345 0.4690869 0.5654074
330 -0.2599211 0.4692808 0.5661446
331 -0.2578076 0.4694747 0.5668767
332 -0.2556942 0.4696646 0.5676039
333 -0.2535808 0.4698500 0.5683259
 [ reached 'max' / getOption("max.print") -- omitted 691 rows ]

$NCV
          x           y
1  3.692550  1.20679238
2  3.656080 -0.95523623
3  4.225980  0.54195552
4  3.590101 -0.12620444
5  3.615422  0.27318687
6  3.974877 -0.64963341
7  3.829947  0.53285662
8  4.126278 -0.44760673
9  3.707318  0.01144034
10 3.722548 -0.38755092

$HOMOGENEITY
          x         y
1  3.692550 1.4171355
2  3.656080 1.2235901
3  4.225980 1.0485540
4  3.590101 0.4685867
5  3.615422 0.6424395
6  3.974877 0.9855162
7  3.829947 1.0001228
8  4.126278 0.8373101
9  3.707318 0.1348002
10 3.722548 0.7422124

$OUTLIERS
OK: No outliers detected.
- Based on the following method and threshold: cook (0.942).
- For variable: (Whole model)


$INFLUENTIAL
         Hat Cooks_Distance Predicted   Residuals Std_Residuals Index Influential
1  0.4313095   7.647131e-01  3.692550  1.20679238    2.00827290     1          OK
2  0.3588878   3.136957e-01  3.656080 -0.95523623   -1.49717276     2          OK
3  0.6173335   4.875314e-01  4.225980  0.54195552    1.09946545     3          OK
4  0.4797096   1.111303e-02  3.590101 -0.12620444   -0.21957349     4          OK
5  0.3100034   1.913324e-02  3.615422  0.27318687    0.41272853     5          OK
6  0.2954077   9.887329e-02  3.974877 -0.64963341   -0.97124221     6          OK
7  0.5530450   3.094924e-01  3.829947  0.53285662    1.00024553     7          OK
8  0.3580455   6.853609e-02  4.126278 -0.44760673   -0.70108818     8          OK
9  0.3757310   4.968294e-05  3.707318  0.01144034    0.01817109     9          OK
10 0.2205269   2.146413e-02  3.722548 -0.38755092   -0.55087917    10          OK

$PP_CHECK

attr(,"class")
[1] "check_model"     "see_check_model"
attr(,"panel")
[1] TRUE
attr(,"dot_size")
[1] 2
attr(,"line_size")
[1] 0.8
attr(,"base_size")
[1] 10
attr(,"axis_title_size")
[1] 10
attr(,"title_size")
[1] 12
attr(,"check")
[1] "all"
attr(,"alpha")
[1] 0.2
attr(,"dot_alpha")
[1] 0.8
attr(,"show_dots")
[1] TRUE
attr(,"detrend")
[1] TRUE
attr(,"colors")
[1] "#3aaf85" "#1b6ca8" "#cd201f"
attr(,"theme")
[1] "see::theme_lucid"
attr(,"model_info")
attr(,"model_info")$is_binomial
[1] FALSE

attr(,"model_info")$is_bernoulli
[1] FALSE

attr(,"model_info")$is_count
[1] FALSE

attr(,"model_info")$is_poisson
[1] FALSE

attr(,"model_info")$is_negbin
[1] FALSE

attr(,"model_info")$is_beta
[1] FALSE

attr(,"model_info")$is_betabinomial
[1] FALSE

attr(,"model_info")$is_orderedbeta
[1] FALSE

attr(,"model_info")$is_dirichlet
[1] FALSE

attr(,"model_info")$is_exponential
[1] FALSE

attr(,"model_info")$is_logit
[1] FALSE

attr(,"model_info")$is_probit
[1] FALSE

attr(,"model_info")$is_censored
[1] FALSE

attr(,"model_info")$is_truncated
[1] FALSE

attr(,"model_info")$is_survival
[1] FALSE

attr(,"model_info")$is_linear
[1] TRUE

attr(,"model_info")$is_tweedie
[1] FALSE

attr(,"model_info")$is_zeroinf
[1] FALSE

attr(,"model_info")$is_zero_inflated
[1] FALSE

attr(,"model_info")$is_dispersion
[1] FALSE

attr(,"model_info")$is_hurdle
[1] FALSE

attr(,"model_info")$is_ordinal
[1] FALSE

attr(,"model_info")$is_cumulative
[1] FALSE

attr(,"model_info")$is_multinomial
[1] FALSE

attr(,"model_info")$is_categorical
[1] FALSE

attr(,"model_info")$is_mixed
[1] FALSE

attr(,"model_info")$is_multivariate
[1] FALSE

attr(,"model_info")$is_trial
[1] FALSE

attr(,"model_info")$is_bayesian
[1] FALSE

attr(,"model_info")$is_gam
[1] FALSE

attr(,"model_info")$is_anova
[1] FALSE

attr(,"model_info")$is_timeseries
[1] FALSE

attr(,"model_info")$is_ttest
[1] FALSE

attr(,"model_info")$is_correlation
[1] FALSE

attr(,"model_info")$is_onewaytest
[1] FALSE

attr(,"model_info")$is_chi2test
[1] FALSE

attr(,"model_info")$is_ranktest
[1] FALSE

attr(,"model_info")$is_levenetest
[1] FALSE

attr(,"model_info")$is_variancetest
[1] FALSE

attr(,"model_info")$is_xtab
[1] FALSE

attr(,"model_info")$is_proptest
[1] FALSE

attr(,"model_info")$is_binomtest
[1] FALSE

attr(,"model_info")$is_ftest
[1] FALSE

attr(,"model_info")$is_meta
[1] FALSE

attr(,"model_info")$link_function
[1] "identity"

attr(,"model_info")$family
[1] "gaussian"

attr(,"model_info")$n_obs
[1] 10

attr(,"model_info")$n_grouplevels
NULL

attr(,"bandwidth")
[1] "nrd"
attr(,"type")
[1] "density"
attr(,"model_class")
[1] "lm"

The results suggested that the current model could be reliable.

4.2. BDF ~ Speaking Anxiety

4.2.1. MCPR ~ Speaking Anxiety

The following code block constructs a regression model between MCPR and speaking anxiety.

model_mcpr <- lm(
  mid_clause_pause_ratio ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety
)

The following code block shows the result.

tab_model(model_mcpr, digits = 3)

The result did not show significant relationship between three anxiety scores and MCPR.

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_mcpr)

Package `patchwork` required for this function to work.

Y

trying URL 'https://packagemanager.posit.co/cran/latest/bin/macosx/big-sur-arm64/contrib/4.4/patchwork_1.3.0.tgz'
Content type 'binary/octet-stream' length 3351486 bytes (3.2 MB)
==================================================
downloaded 3.2 MB

The downloaded binary packages are in
    /var/folders/kp/vjrts6q502j2d5hzlbh2q8900000gp/T//RtmpDQ6I8w/downloaded_packages

The results suggested that the current model could be less reliable because the model could be affected by an outlier.

4.2.2. ECPR ~ Speaking Anxiety

The following code block constructs a regression model between ECPR and speaking anxiety.

model_ecpr <- lm(
  end_clause_pause_ratio ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety
)

The following code block shows the result.

tab_model(model_ecpr, digits = 3)

The result showed slightly significant relationship between cognitive anxiety and ECPR (\(p=.081\)). The slope was \(-.003\) and suggested that ECPR decreased \(.003\) when cognitive anxiety increased \(1\).

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ecpr)

The results suggested that the current model could be reliable.

4.2.3. MCPD ~ Speaking Anxiety

The following code block constructs a regression model between MCPD and speaking anxiety.

model_mcpd <- lm(
  mid_clause_p.dur ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety
)

The following code block shows the result.

tab_model(model_mcpd, digits = 3)

The result showed a significant link between behavioral anxiety and MCPD (\(p=.025\)). The slope was \(-.074\), suggesting that MCPD became \(.074\) shorter when behavioral anxiety score increased \(1\).

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_mcpd)

The results suggested that the current model could be reliable.

4.2.4. ECPD ~ Speaking Anxiety

The following code block constructs a regression model between AR and speaking anxiety.

model_ecpd <- lm(
  end_clause_p.dur ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety
)

The following code block shows the result.

tab_model(model_ecpd, digits = 3)

The result showed a significant link between behavioral anxiety and MCPD (\(p=.020\)). The slope was \(-.072\), suggesting that ECPD became \(.072\) shorter when behavioral anxiety score increased \(1\).

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ecpd)

The results suggested that the current model could be reliable.

4.3. RF ~ Speaking Anxiety

The following code block constructs a regression model between DR and speaking anxiety.

model_dr <- lm(
  disfluency_ratio ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety
)

The following code block shows the result.

tab_model(model_dr, digits = 3)

The result did not show significant relationship between three anxiety scores and DR.

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_dr)

The results suggested that the current model could be less reliable because the model could be affected by an outlier.

The following code block shows the summary of regression models.

tab_model(
  model_ar,
  model_mcpr,
  model_ecpr,
  model_mcpd,
  model_ecpd,
  model_dr,
  dv.labels = c("AR", "MCPR", "ECPR", "MCPD", "ECPD", "DR"),
  pred.labels = c("(Intercept)", "CA", "SA", "BA"),
  digits = 3
)

df_uf_anxiety %>%
  select(c(
    cognitive_anxiety,
    articulation_rate
  )) %>%
  chart.Correlation(histogram = F, method = "pearson", pch = 19)

df_uf_anxiety %>%
  select(c(
    cognitive_anxiety,
    mid_clause_p.dur
  )) %>%
  chart.Correlation(histogram = F, method = "pearson", pch = 19)

df_uf_anxiety %>%
  select(c(
    cognitive_anxiety,
    articulation_rate,
    mid_clause_p.dur,
    end_clause_p.dur
  )) %>%
  pairs(panel = panel.smooth, pch = 19)

plot(
  df_uf_anxiety$cognitive_anxiety, 
  df_uf_anxiety$articulation_rate,
  pch = 19,
  xlab = "Cognitive Anxiety",
  ylab = "Articulation Rate"
)
lines(
  lowess(
    df_uf_anxiety$cognitive_anxiety, 
    df_uf_anxiety$articulation_rate
  ), 
  col = 2
)

plot(
  df_uf_anxiety$cognitive_anxiety, 
  df_uf_anxiety$mid_clause_p.dur,
  pch = 19,
  xlab = "Cognitive Anxiety",
  ylab = "Mid-Clause Pause Duration"
)
lines(
  lowess(
    df_uf_anxiety$cognitive_anxiety, 
    df_uf_anxiety$mid_clause_p.dur
  ), 
  col = 2
)

plot(
  df_uf_anxiety$cognitive_anxiety, 
  df_uf_anxiety$end_clause_p.dur,
  pch = 19,
  xlab = "Cognitive Anxiety",
  ylab = "End-Clause Pause Duration"
)
lines(
  lowess(
    df_uf_anxiety$cognitive_anxiety, 
    df_uf_anxiety$end_clause_p.dur
  ), 
  col = 2
)